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In three dimensions, a parallelepiped is a prism whose faces are all parallelograms. Let A, B, and C be the basis vectors defining a three-dimensional parallelepiped. Then ...

Let DeltaH_AH_BH_C be the orthic triangle of a triangle DeltaABC. Then each side of each triangle meets the three sides of the other triangle, and the points of intersection ...

The x- (horizontal) coordinate of a point in a two dimensional coordinate system. Physicists and astronomers sometimes use the term to refer to the axis itself instead of the ...

The usual type of vector, which can be viewed as a contravariant tensor ("ket") of tensor rank 1. Contravariant vectors are dual to one-forms ("bras," a.k.a. covariant ...

Let J_A, J_B, and J_C be the vertices of the outer Soddy triangle, and also let E_A, E_B, and E_C be the pairwise contact points of the three tangent circles. Then the lines ...

The gnomonic projection is a nonconformal map projection obtained by projecting points P_1 (or P_2) on the surface of sphere from a sphere's center O to point P in a plane ...

Let I_A, I_B, and I_C be the vertices of the inner Soddy triangle, and also let E_A, E_B, and E_C be the pairwise contact points of the three tangent circles. Then the lines ...

A subset {v_1,...,v_k} of a vector space V, with the inner product <,>, is called orthogonal if <v_i,v_j>=0 when i!=j. That is, the vectors are mutually perpendicular. Note ...

Functional analysis is a branch of mathematics concerned with infinite-dimensional vector spaces (mainly function spaces) and mappings between them. The spaces may be of ...

int_a^b(del f)·ds=f(b)-f(a), where del is the gradient, and the integral is a line integral. It is this relationship which makes the definition of a scalar potential function ...